SP500_prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from datetime import datetime\n",
    "import seaborn as sns\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.ensemble import BaggingRegressor\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "from sklearn.metrics import r2_score\n",
    "import matplotlib.pyplot as plt\n",
    "pd.options.display.max_rows = 2500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_folder = './data/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### S&P500\n",
    "#### Source: https://finance.yahoo.com/quote/%5EGSPC/history?period1=1242878400&period2=1558411200&interval=1d&filter=history&frequency=1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 568,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>S&amp;P500</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2009-05-21</td>\n",
       "      <td>888.330017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2009-05-22</td>\n",
       "      <td>887.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2009-05-26</td>\n",
       "      <td>910.330017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2009-05-27</td>\n",
       "      <td>893.059998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2009-05-28</td>\n",
       "      <td>906.830017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date      S&P500\n",
       "0 2009-05-21  888.330017\n",
       "1 2009-05-22  887.000000\n",
       "2 2009-05-26  910.330017\n",
       "3 2009-05-27  893.059998\n",
       "4 2009-05-28  906.830017"
      ]
     },
     "execution_count": 568,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SP500 = pd.read_csv(data_folder+'S&P500_source.csv')\n",
    "SP500 = SP500[['Date','Close']]\n",
    "SP500.columns = ['Date','S&P500']\n",
    "SP500['Date'] = pd.to_datetime(SP500['Date'])\n",
    "SP500.to_csv(data_folder+'S&P500.csv',index = False)\n",
    "SP500.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Consumer Price Index\n",
    "#### Source: https://data.oecd.org/price/inflation-cpi.htm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 569,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>CPI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3291</th>\n",
       "      <td>2009-03-01</td>\n",
       "      <td>-0.383556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3292</th>\n",
       "      <td>2009-04-01</td>\n",
       "      <td>-0.736886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3293</th>\n",
       "      <td>2009-05-01</td>\n",
       "      <td>-1.281436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3294</th>\n",
       "      <td>2009-06-01</td>\n",
       "      <td>-1.426776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3295</th>\n",
       "      <td>2009-07-01</td>\n",
       "      <td>-2.097161</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Date       CPI\n",
       "3291 2009-03-01 -0.383556\n",
       "3292 2009-04-01 -0.736886\n",
       "3293 2009-05-01 -1.281436\n",
       "3294 2009-06-01 -1.426776\n",
       "3295 2009-07-01 -2.097161"
      ]
     },
     "execution_count": 569,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CPI = pd.read_csv(data_folder+'CPI_source.csv')\n",
    "CPI = CPI[CPI['LOCATION']=='USA'][['TIME','Value']]#Took the decision to use only US data\n",
    "CPI.columns = ['Date','CPI']\n",
    "CPI['Date'] = pd.to_datetime(CPI['Date'])\n",
    "CPI.to_csv(data_folder+'CPI.csv',index = False) \n",
    "CPI.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unemployement Rate\n",
    "#### Source: https://data.bls.gov/timeseries/lns14000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 570,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>UR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2009-01-01</td>\n",
       "      <td>7,8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2009-02-01</td>\n",
       "      <td>8,3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2009-03-01</td>\n",
       "      <td>8,7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2009-04-01</td>\n",
       "      <td>9,0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2009-05-01</td>\n",
       "      <td>9,4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "        Date   UR\n",
       "0 2009-01-01  7,8\n",
       "1 2009-02-01  8,3\n",
       "2 2009-03-01  8,7\n",
       "3 2009-04-01  9,0\n",
       "4 2009-05-01  9,4"
      ]
     },
     "execution_count": 570,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UR_tab = pd.read_csv(data_folder+'UR_source.csv',sep=';')\n",
    "#Convert the matrix into a dataframe\n",
    "years = np.repeat(UR_tab.Year.values,[12]*11)\n",
    "months = ['01','02','03','04','05','06','07','08','09','10','11','12']*11\n",
    "values = UR_tab.drop(columns = ['Year']).values.ravel()\n",
    "data = {'year': years, 'month':months, 'UR':values}\n",
    "UR = pd.DataFrame(data = data)\n",
    "#Add date column\n",
    "UR['Date'] = UR.apply(lambda x: str(x['year'])+'-'+x['month'],axis = 1)\n",
    "UR = UR[['Date','UR']]\n",
    "UR['Date'] = pd.to_datetime(UR['Date'])\n",
    "UR.to_csv(data_folder+'UR.csv',index = False)\n",
    "UR.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Purchasing Management Index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 571,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>PMI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>732</th>\n",
       "      <td>2009-01-01</td>\n",
       "      <td>34,9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>733</th>\n",
       "      <td>2009-02-01</td>\n",
       "      <td>35,5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>734</th>\n",
       "      <td>2009-03-01</td>\n",
       "      <td>36,0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>735</th>\n",
       "      <td>2009-04-01</td>\n",
       "      <td>39,5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>736</th>\n",
       "      <td>2009-05-01</td>\n",
       "      <td>41,7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Date   PMI\n",
       "732 2009-01-01  34,9\n",
       "733 2009-02-01  35,5\n",
       "734 2009-03-01  36,0\n",
       "735 2009-04-01  39,5\n",
       "736 2009-05-01  41,7"
      ]
     },
     "execution_count": 571,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PMI = pd.read_csv(data_folder+'PMI_source.csv',sep=';')\n",
    "PMI.columns =['Date','PMI']\n",
    "PMI['Date'] = pd.to_datetime(PMI['Date'])\n",
    "PMI = PMI[PMI['Date']>=datetime.strptime('2009-01-01','%Y-%m-%d')]\n",
    "PMI.to_csv(data_folder+'PMI.csv',index = False)\n",
    "PMI.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nikkei 225 index\n",
    "#### Source: https://finance.yahoo.com/quote/%5EN225/history?period1=1242792000&period2=1558324800&interval=1d&filter=history&frequency=1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 572,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Nikkei225</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2009-05-20</td>\n",
       "      <td>9344.639648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2009-05-21</td>\n",
       "      <td>9264.150391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2009-05-22</td>\n",
       "      <td>9225.809570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2009-05-25</td>\n",
       "      <td>9347.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2009-05-26</td>\n",
       "      <td>9310.809570</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date    Nikkei225\n",
       "0 2009-05-20  9344.639648\n",
       "1 2009-05-21  9264.150391\n",
       "2 2009-05-22  9225.809570\n",
       "3 2009-05-25  9347.000000\n",
       "4 2009-05-26  9310.809570"
      ]
     },
     "execution_count": 572,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Nikkei225 = pd.read_csv(data_folder+'Nikkei225_source.csv')\n",
    "Nikkei225 = Nikkei225[['Date','Close']]\n",
    "Nikkei225.columns = ['Date','Nikkei225']\n",
    "Nikkei225['Date'] = pd.to_datetime(Nikkei225['Date'])\n",
    "Nikkei225.to_csv(data_folder+'Nikkei225.csv',index = False)\n",
    "Nikkei225.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Volatility Index\n",
    "#### Source: https://finance.yahoo.com/quote/%5EVIX/history?period1=1242792000&period2=1558324800&interval=1d&filter=history&frequency=1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 573,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>VIX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2009-05-20</td>\n",
       "      <td>29.030001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2009-05-21</td>\n",
       "      <td>31.350000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2009-05-22</td>\n",
       "      <td>32.630001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2009-05-26</td>\n",
       "      <td>30.620001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2009-05-27</td>\n",
       "      <td>32.360001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "        Date        VIX\n",
       "0 2009-05-20  29.030001\n",
       "1 2009-05-21  31.350000\n",
       "2 2009-05-22  32.630001\n",
       "3 2009-05-26  30.620001\n",
       "4 2009-05-27  32.360001"
      ]
     },
     "execution_count": 573,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VIX = pd.read_csv(data_folder+'VIX_source.csv')\n",
    "VIX = VIX[['Date','Close']]\n",
    "VIX.columns = ['Date','VIX']\n",
    "VIX['Date'] = pd.to_datetime(VIX['Date'])\n",
    "VIX.to_csv(data_folder+'VIX.csv',index = False)\n",
    "VIX.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effective Federal Fund Rate\n",
    "#### Source: https://apps.newyorkfed.org/markets/autorates/fed-funds-search-result-page"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 574,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>EFFR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>2,39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>2,39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>2,39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>2,4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2019-05-14</td>\n",
       "      <td>2,38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date  EFFR\n",
       "0 2019-05-20  2,39\n",
       "1 2019-05-17  2,39\n",
       "2 2019-05-16  2,39\n",
       "3 2019-05-15   2,4\n",
       "4 2019-05-14  2,38"
      ]
     },
     "execution_count": 574,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#EFFR\n",
    "#Source: https://apps.newyorkfed.org/markets/autorates/fed-funds-search-result-page\n",
    "EFFR = pd.read_csv(data_folder+'EFFR_source.csv',sep=';')\n",
    "EFFR.columns = ['Date','Volume','EFFR']\n",
    "EFFR.drop(columns = ['Volume'],inplace = True)\n",
    "EFFR = EFFR.iloc[0:2514]\n",
    "def convert_date(date):\n",
    "    try:\n",
    "        return(datetime.strptime(date,'%d/%m/%Y'))\n",
    "    except:\n",
    "        return(datetime.strptime(date,'%Y-%m-%d[r]'))\n",
    "EFFR['Date'] = EFFR['Date'].apply(lambda x: convert_date(x))\n",
    "EFFR.to_csv(data_folder+'EFFR.csv',index = False)\n",
    "EFFR.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### VIX Votality Index\n",
    "#### Source: https://finance.yahoo.com/quote/%5EVVIX/history?period1=1242792000&period2=1558324800&interval=1d&filter=history&frequency=1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 575,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>VVIX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2009-05-20</td>\n",
       "      <td>77.449997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2009-05-21</td>\n",
       "      <td>84.690002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2009-05-22</td>\n",
       "      <td>87.279999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2009-05-26</td>\n",
       "      <td>91.230003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2009-05-27</td>\n",
       "      <td>90.860001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date       VVIX\n",
       "0 2009-05-20  77.449997\n",
       "1 2009-05-21  84.690002\n",
       "2 2009-05-22  87.279999\n",
       "3 2009-05-26  91.230003\n",
       "4 2009-05-27  90.860001"
      ]
     },
     "execution_count": 575,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#VVIX\n",
    "#Source: https://finance.yahoo.com/quote/%5EVVIX/history?period1=1242792000&period2=1558324800&interval=1d&filter=history&frequency=1d\n",
    "VVIX = pd.read_csv(data_folder+'VVIX_source.csv')\n",
    "VVIX = VVIX[['Date','Close']]\n",
    "VVIX.columns = ['Date','VVIX']\n",
    "VVIX['Date'] = pd.to_datetime(VVIX['Date'])\n",
    "VVIX.to_csv(data_folder+'VVIX.csv',index = False)\n",
    "VVIX.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Processing\n",
    "#### Set Date as index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 577,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write you data processing code below\n",
    "SP500.set_index('Date',inplace = True)\n",
    "CPI.set_index('Date',inplace = True)\n",
    "UR.set_index('Date',inplace = True)\n",
    "PMI.set_index('Date',inplace = True)\n",
    "Nikkei225.set_index('Date',inplace = True)\n",
    "VIX.set_index('Date',inplace = True)\n",
    "EFFR.set_index('Date',inplace = True)\n",
    "VVIX.set_index('Date',inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Concatenate all the databases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 578,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.concat([SP500,CPI,UR,PMI,Nikkei225,VIX,EFFR,VVIX],axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 579,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S&amp;P500</th>\n",
       "      <th>CPI</th>\n",
       "      <th>UR</th>\n",
       "      <th>PMI</th>\n",
       "      <th>Nikkei225</th>\n",
       "      <th>VIX</th>\n",
       "      <th>EFFR</th>\n",
       "      <th>VVIX</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2009-01-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7,8</td>\n",
       "      <td>34,9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-02-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8,3</td>\n",
       "      <td>35,5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-03-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.383556</td>\n",
       "      <td>8,7</td>\n",
       "      <td>36,0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-04-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.736886</td>\n",
       "      <td>9,0</td>\n",
       "      <td>39,5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-05-01</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.281436</td>\n",
       "      <td>9,4</td>\n",
       "      <td>41,7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-05-20</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9344.639648</td>\n",
       "      <td>29.030001</td>\n",
       "      <td>0,14</td>\n",
       "      <td>77.449997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-05-21</th>\n",
       "      <td>888.330017</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9264.150391</td>\n",
       "      <td>31.350000</td>\n",
       "      <td>0,17</td>\n",
       "      <td>84.690002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-05-22</th>\n",
       "      <td>887.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9225.809570</td>\n",
       "      <td>32.630001</td>\n",
       "      <td>0,17</td>\n",
       "      <td>87.279999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-05-25</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9347.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-05-26</th>\n",
       "      <td>910.330017</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9310.809570</td>\n",
       "      <td>30.620001</td>\n",
       "      <td>0,18</td>\n",
       "      <td>91.230003</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                S&P500       CPI   UR   PMI    Nikkei225        VIX  EFFR  \\\n",
       "Date                                                                        \n",
       "2009-01-01         NaN       NaN  7,8  34,9          NaN        NaN   NaN   \n",
       "2009-02-01         NaN       NaN  8,3  35,5          NaN        NaN   NaN   \n",
       "2009-03-01         NaN -0.383556  8,7  36,0          NaN        NaN   NaN   \n",
       "2009-04-01         NaN -0.736886  9,0  39,5          NaN        NaN   NaN   \n",
       "2009-05-01         NaN -1.281436  9,4  41,7          NaN        NaN   NaN   \n",
       "2009-05-20         NaN       NaN  NaN   NaN  9344.639648  29.030001  0,14   \n",
       "2009-05-21  888.330017       NaN  NaN   NaN  9264.150391  31.350000  0,17   \n",
       "2009-05-22  887.000000       NaN  NaN   NaN  9225.809570  32.630001  0,17   \n",
       "2009-05-25         NaN       NaN  NaN   NaN  9347.000000        NaN   NaN   \n",
       "2009-05-26  910.330017       NaN  NaN   NaN  9310.809570  30.620001  0,18   \n",
       "\n",
       "                 VVIX  \n",
       "Date                   \n",
       "2009-01-01        NaN  \n",
       "2009-02-01        NaN  \n",
       "2009-03-01        NaN  \n",
       "2009-04-01        NaN  \n",
       "2009-05-01        NaN  \n",
       "2009-05-20  77.449997  \n",
       "2009-05-21  84.690002  \n",
       "2009-05-22  87.279999  \n",
       "2009-05-25        NaN  \n",
       "2009-05-26  91.230003  "
      ]
     },
     "execution_count": 579,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 580,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2652"
      ]
     },
     "execution_count": 580,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Filling the monthly features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 581,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[['CPI','UR','PMI']] = data[['CPI','UR','PMI']].ffill()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Drop the remaining NaNs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 582,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 583,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2356"
      ]
     },
     "execution_count": 583,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Replace str values by floats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 584,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.UR = data.UR.apply(lambda x: float(x.replace(',','.')))\n",
    "data.PMI = data.PMI.apply(lambda x:float(x.replace(',','.')))\n",
    "data.EFFR = data.EFFR.apply(lambda x:float(x.replace(',','.')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Outliers handling\n",
    "#### S&P500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 585,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data['S&P500'])\n",
    "plt.title('S&P500 values distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the distribution there are no outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### CPI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 586,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data.CPI)\n",
    "plt.title('CPI values distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are some outliers in the negative values. I will drop those under 3 standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 587,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of rows below 3 std: 21\n"
     ]
    }
   ],
   "source": [
    "CPIstd = data.CPI.std()\n",
    "CPImu = data.CPI.mean()\n",
    "print('number of rows below 3 std:',data[(data.CPI < CPImu-3*CPIstd)].shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 588,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data[(data.CPI >= CPImu-3*CPIstd)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 589,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of rows above 3 std: 0\n"
     ]
    }
   ],
   "source": [
    "print('number of rows above 3 std:',data[(data.CPI > CPImu+3*CPIstd)].shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unemployement Rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 591,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data.UR)\n",
    "plt.title('Unemployement Rate values distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No outlier appearing in the distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### PMI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 593,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data.PMI)\n",
    "plt.title('PMI values distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 594,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of rows below 3 std: 6\n"
     ]
    }
   ],
   "source": [
    "PMIstd = data.PMI.std()\n",
    "PMImu = data.PMI.mean()\n",
    "print('number of rows below 3 std:',data[(data.PMI < PMImu-3*PMIstd)].shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 595,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data[(data.PMI >= PMImu-3*PMIstd)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 597,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of rows above 3 std: 0\n"
     ]
    }
   ],
   "source": [
    "print('number of rows above 3 std:',data[(data.PMI > PMImu+3*PMIstd)].shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Nikkei 225 index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 598,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 598,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data.Nikkei225)\n",
    "plt.title('Nikkei225 values distribution')\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No outliers appearing in the distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### VIX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 599,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data.VIX)\n",
    "plt.title('VIX values distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution is very clean I won't drop any outlier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EFFR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 602,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data.EFFR)\n",
    "plt.title('EFFR values distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to the particularity of the distribution I won't drop any outlier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### VVIX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 601,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6499: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data.VVIX)\n",
    "plt.title('VVIX values distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution is very clean, no outliers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 603,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S&amp;P500</th>\n",
       "      <th>CPI</th>\n",
       "      <th>UR</th>\n",
       "      <th>PMI</th>\n",
       "      <th>Nikkei225</th>\n",
       "      <th>VIX</th>\n",
       "      <th>EFFR</th>\n",
       "      <th>VVIX</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2009-06-01</th>\n",
       "      <td>942.869995</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9677.750000</td>\n",
       "      <td>30.040001</td>\n",
       "      <td>0.21</td>\n",
       "      <td>84.230003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-02</th>\n",
       "      <td>944.739990</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9704.309570</td>\n",
       "      <td>29.629999</td>\n",
       "      <td>0.20</td>\n",
       "      <td>83.820000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-03</th>\n",
       "      <td>931.760010</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9741.669922</td>\n",
       "      <td>31.020000</td>\n",
       "      <td>0.21</td>\n",
       "      <td>84.889999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-04</th>\n",
       "      <td>942.460022</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9668.959961</td>\n",
       "      <td>30.180000</td>\n",
       "      <td>0.20</td>\n",
       "      <td>81.260002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-05</th>\n",
       "      <td>940.090027</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9768.009766</td>\n",
       "      <td>29.620001</td>\n",
       "      <td>0.21</td>\n",
       "      <td>82.110001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                S&P500       CPI   UR   PMI    Nikkei225        VIX  EFFR  \\\n",
       "Date                                                                        \n",
       "2009-06-01  942.869995 -1.426776  9.5  45.8  9677.750000  30.040001  0.21   \n",
       "2009-06-02  944.739990 -1.426776  9.5  45.8  9704.309570  29.629999  0.20   \n",
       "2009-06-03  931.760010 -1.426776  9.5  45.8  9741.669922  31.020000  0.21   \n",
       "2009-06-04  942.460022 -1.426776  9.5  45.8  9668.959961  30.180000  0.20   \n",
       "2009-06-05  940.090027 -1.426776  9.5  45.8  9768.009766  29.620001  0.21   \n",
       "\n",
       "                 VVIX  \n",
       "Date                   \n",
       "2009-06-01  84.230003  \n",
       "2009-06-02  83.820000  \n",
       "2009-06-03  84.889999  \n",
       "2009-06-04  81.260002  \n",
       "2009-06-05  82.110001  "
      ]
     },
     "execution_count": 603,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 605,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first date of data is: 2009-06-01 00:00:00\n",
      "The last date of data is: 2019-05-20 00:00:00\n"
     ]
    }
   ],
   "source": [
    "print('The first date of data is:',data.index.min())\n",
    "print('The last date of data is:',data.index.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 608,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We have here 3640 days of data which almost 10 years\n"
     ]
    }
   ],
   "source": [
    "print('We have here',(data.index.max()-data.index.min()).days,'days of data which almost 10 years')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding Feature and shifting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adding return for S&P500 and Nikkei 225 and shifting everything to predict next day's return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 609,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S&amp;P500</th>\n",
       "      <th>CPI</th>\n",
       "      <th>UR</th>\n",
       "      <th>PMI</th>\n",
       "      <th>Nikkei225</th>\n",
       "      <th>VIX</th>\n",
       "      <th>EFFR</th>\n",
       "      <th>VVIX</th>\n",
       "      <th>S&amp;P_return</th>\n",
       "      <th>Nikkei225_return_d1</th>\n",
       "      <th>S&amp;P_return_d1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2009-06-01</th>\n",
       "      <td>942.869995</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9677.750000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-02</th>\n",
       "      <td>944.739990</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9704.309570</td>\n",
       "      <td>30.040001</td>\n",
       "      <td>0.21</td>\n",
       "      <td>84.230003</td>\n",
       "      <td>0.001983</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-03</th>\n",
       "      <td>931.760010</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9741.669922</td>\n",
       "      <td>29.629999</td>\n",
       "      <td>0.20</td>\n",
       "      <td>83.820000</td>\n",
       "      <td>-0.013739</td>\n",
       "      <td>0.002744</td>\n",
       "      <td>0.001983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-04</th>\n",
       "      <td>942.460022</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9668.959961</td>\n",
       "      <td>31.020000</td>\n",
       "      <td>0.21</td>\n",
       "      <td>84.889999</td>\n",
       "      <td>0.011484</td>\n",
       "      <td>0.003850</td>\n",
       "      <td>-0.013739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-06-05</th>\n",
       "      <td>940.090027</td>\n",
       "      <td>-1.426776</td>\n",
       "      <td>9.5</td>\n",
       "      <td>45.8</td>\n",
       "      <td>9768.009766</td>\n",
       "      <td>30.180000</td>\n",
       "      <td>0.20</td>\n",
       "      <td>81.260002</td>\n",
       "      <td>-0.002515</td>\n",
       "      <td>-0.007464</td>\n",
       "      <td>0.011484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                S&P500       CPI   UR   PMI    Nikkei225        VIX  EFFR  \\\n",
       "Date                                                                        \n",
       "2009-06-01  942.869995       NaN  NaN   NaN  9677.750000        NaN   NaN   \n",
       "2009-06-02  944.739990 -1.426776  9.5  45.8  9704.309570  30.040001  0.21   \n",
       "2009-06-03  931.760010 -1.426776  9.5  45.8  9741.669922  29.629999  0.20   \n",
       "2009-06-04  942.460022 -1.426776  9.5  45.8  9668.959961  31.020000  0.21   \n",
       "2009-06-05  940.090027 -1.426776  9.5  45.8  9768.009766  30.180000  0.20   \n",
       "\n",
       "                 VVIX  S&P_return  Nikkei225_return_d1  S&P_return_d1  \n",
       "Date                                                                   \n",
       "2009-06-01        NaN         NaN                  NaN            NaN  \n",
       "2009-06-02  84.230003    0.001983                  NaN            NaN  \n",
       "2009-06-03  83.820000   -0.013739             0.002744       0.001983  \n",
       "2009-06-04  84.889999    0.011484             0.003850      -0.013739  \n",
       "2009-06-05  81.260002   -0.002515            -0.007464       0.011484  "
      ]
     },
     "execution_count": 609,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['S&P_return'] = data['S&P500']/data['S&P500'].shift(1) -1\n",
    "data['Nikkei225_return_d1'] = (data.Nikkei225/data.Nikkei225.shift(1) -1).shift(1)\n",
    "data['S&P_return_d1'] = data['S&P_return'].shift(1)\n",
    "data[['CPI','UR','PMI','VIX','EFFR','VVIX']] = data[['CPI','UR','PMI','VIX','EFFR','VVIX']].shift(1)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 610,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 611,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The final number of rows is: 2327\n"
     ]
    }
   ],
   "source": [
    "print('The final number of rows is:',data.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define a functiun to split the data between train, validation and test set "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_val_test_split(X,Y,test_size,val=False,val_size=None):\n",
    "    n = len(Y)\n",
    "    if val:\n",
    "        Y_train = Y[:int(n*(1-val_size-test_size))]\n",
    "        Y_val = Y[int(n*(1-val_size-test_size)):int(n*(1-val_size-test_size))+int(n*val_size)]\n",
    "        Y_test = Y[int(n*(1-val_size-test_size))+int(n*val_size):]\n",
    "        X_train = X[:int(n*(1-val_size-test_size))]\n",
    "        X_val = X[int(n*(1-val_size-test_size)):int(n*(1-val_size-test_size))+int(n*val_size)]\n",
    "        X_test = X[int(n*(1-val_size-test_size))+int(n*val_size):]\n",
    "        return([Y_train,X_train, Y_val, X_val, Y_test, X_test])\n",
    "    else:\n",
    "        Y_train = Y[:int(n*(1-test_size))]\n",
    "        Y_test = Y[int(n*(1-test_size)):]\n",
    "        X_train = X[:int(n*(1-test_size))]\n",
    "        X_test = X[int(n*(1-test_size)):]\n",
    "        return([Y_train, X_train, Y_test, X_test])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define a function to compute the money made by investing 1 dollar at the begining of the testing period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "metadata": {},
   "outputs": [],
   "source": [
    "def money_made(Y_pred, Y_test):\n",
    "    true_pred = (np.sign(Y_pred) == np.sign(Y_test))\n",
    "    val = 1\n",
    "    for i in range(len(Y_test)):\n",
    "        if true_pred[i]:\n",
    "            val = val*(1+abs(Y_test[i]))\n",
    "        else:\n",
    "            val = val*(1-abs(Y_test[i]))\n",
    "    return val"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### define X Covariates and Y the independent variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = data['S&P_return'].values\n",
    "X = data.drop(columns = ['S&P_return','S&P500','Nikkei225','Nikkei225_return']).values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 617,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "begining of test set is: 2017-06-01 00:00:00\n"
     ]
    }
   ],
   "source": [
    "print('begining of test set is:',data.index[int(len(Y)*0.8)+1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 672,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train, X_train, Y_test, X_test = train_val_test_split(X,Y,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 673,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 673,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 674,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 675,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R² score for this model is: 0.10605669305600374\n"
     ]
    }
   ],
   "source": [
    "r2_lin = r2_score(Y_test,Y_pred)\n",
    "print('The R² score for this model is:',r2_lin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 677,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Investing $1 the first if June 2017 will give now 2.1925203345209545 $\n"
     ]
    }
   ],
   "source": [
    "money_lin = money_made(Y_pred,Y_test)\n",
    "print('Investing $1 the first if June 2017 will give now',money_lin,'$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lasso Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I run a validation test to find the best alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 619,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train, X_train, Y_val, X_val, Y_test, X_test = train_val_test_split(X,Y,test_size = 0.2,val = True, val_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 620,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.array([0.0001,0.001,0.01,0.1,1,10,100,1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 621,
   "metadata": {},
   "outputs": [],
   "source": [
    "money = []\n",
    "r2 = []\n",
    "for alpha in alphas:\n",
    "    model = Lasso(alpha = alpha,random_state = 12)\n",
    "    model.fit(X_train,Y_train)\n",
    "    Y_pred = model.predict(X_val)\n",
    "    r2.append(r2_score(Y_val,Y_pred))\n",
    "    money.append(money_made(Y_pred,Y_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 629,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1,2,1)\n",
    "plt.plot(np.log(alphas),money,'r')\n",
    "plt.title(('Money over alpha'))\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(np.log(alphas),r2,'r')\n",
    "plt.title(('R² score over alpha'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {},
   "outputs": [],
   "source": [
    "best_alpha = alphas[np.argmax(np.array(r2))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 678,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best alpha is: 0.001\n"
     ]
    }
   ],
   "source": [
    "print('The best alpha is:',best_alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training the best model on the train + validation set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 679,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train, X_train, Y_test, X_test = train_val_test_split(X,Y,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 680,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=0.001, copy_X=True, fit_intercept=True, max_iter=1000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=12,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False)"
      ]
     },
     "execution_count": 680,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = Lasso(alpha = best_alpha, random_state = 12)\n",
    "model.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 681,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 682,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R² score for this model is: 0.10803186021899625\n"
     ]
    }
   ],
   "source": [
    "r2_las = r2_score(Y_test,Y_pred)\n",
    "print('The R² score for this model is:',r2_las)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 683,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The money made with this model is $ 2.3299686314013215\n"
     ]
    }
   ],
   "source": [
    "money_las = money_made(Y_pred,Y_test)\n",
    "print('The money made with this model is $',money_las)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bagging Regressor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I will only try the bagging regressor with decision tree and do a validation test to find the best number of trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 637,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train, X_train, Y_val, X_val, Y_test, X_test = train_val_test_split(X,Y,test_size = 0.2,val = True, val_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 638,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_estimators = np.arange(10,200,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 643,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2 = []\n",
    "for n in nb_estimators: \n",
    "    model = BaggingRegressor(n_estimators = n,random_state = 12)\n",
    "    model.fit(X_train,Y_train)\n",
    "    Y_pred = model.predict(X_val)\n",
    "    r2.append(r2_score(Y_val, Y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 644,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KWh596xMWTxvGtJTQnC006hsVwd2XTCe/tJI/r7VO9owJV8GeMdwErFHVVGCNO96EiMQDtwOnAnOA2/0SyK9VdQpwMnC6iJwfZDwmSA+/tYuy6jp+FOKzhUZzxw/li7NG8ND6XeQUWid7xoSjYBPDEmCZO7wMuCRAmUXAKlUtUdVSYBWwWFUrVHUtgKrWAJuAkUHGY4JQerSGx97O48IThzN1+MBO285/XzCV/n2juPWlbahaJ3vGhJtgE0Oyqh4AcJ+TApQZAez1G893px0jIoOBi3DOOgISketEJENEMnw+X5Bhm0D+nr6LozWdd7bQKCE2mp8vnsJ7u0p48cN9nbotY0z7tZoYRGS1iGwL8FjSxm189h9d4NjPRBGJAp4G/qiqu1paiao+pKppqpqWmJjYxk2btio5WsPj7+Tx+ZNSmJQc1+nbu/KUUZw8ejD3/udjDlfUdvr2jDFt12piUNUFqjo9wONloEBEhgO4z4UBVpEPjPIbHwns9xt/CMhW1d93/GWYYP1tfS6VtfX8aP7ELtleRIRwzyXTKa2o4ZcrrZM9Y8JJsFVJy4Gl7vBS4OUAZVYC54nIEPei83nuNETkHmAQcH2QcZggFJVX8493drNkRgoTkzr/bKHRtJRBXP25cTz1wR5ueGYz7+0qtmsOxoSBqCCXvw94VkSuAfYAlwOISBrwHVW9VlVLRORuYIO7zF3utJHALcAOYJP7H8J/VtWHg4zJtNPf3syluq6eH87v3GsLgdy4aBL1DQ28sGkfL364j3EJA7jilFFcOmskiXHRXR5PMHYWlJGeXURCbF8S46JJHhhD8sAYYqOD/Zp1vZKjNcT0iaB/3+4XuwmedMdfaGlpaZqRkeF1GD1CYVkVZ/1yLRecOJzffmmmZ3FU1tTz2kcHeGbDXj7IKyEqQpg/NYkrTxnNWZMSiYwIdKkqPNTUNfCXtTn8dV0OtfWf/T4N6BtJ8sAYkgZ+miyS3MSR5JdA+vWN9CD6T+0tqWBl5kFezyxgw+4SxiUM4JnrTut2Cdq0TEQ2qmpaq+UsMfRud72ynWXv5rHmx2czNmGA1+EAkFNYzr8z9vLcxnyKj9YwfFAMl88eyeVpoxgV39/r8JrYsvcQP3tuK1kFZVwyM4UbF02mqraBwiNVFJZVU3CkioIj1RSUVVHYOHykiuq6z3ZBHhcTRfLAGMbE92f22CHMGRvPiSMHER3VOQlDVckpLGfFtoOs3H6QbfuOADBlWBxnTEzgyff3MDq+P09fN5f4AX07JQbTtSwxmFYVHHHOFi6akcKvL5/hdTifUVPXwJqPC/jXhr2sz3aaKJ8xMYErThnFwhOSO+2A2RaVNfX8bvVOHk7fRVJcDP/7xemcOyW5TcuqKkcq6ygoqzqWOArLqih0k0ZWQRm7fEcB527xGSMHkTY2nlPGDmH26HgG9e/T4bhVlS35h1mZeZCV2w6yq8jZzqzRg1k0bRiLpg079gPhnZwivvH4BiYmxfLUtXOD2q4JD5YYTKvuWJ7JP9/bzdqfzGP00PD6Jd7cvkOV/DtjL89u2Mv+w1UM6d+HL84ayZWnjCK1C5rX+ntvVzE3Pb+VvOIKvjxnNDdfMIWBMaE9aBaXV7Nxdykb8krYkFfKtn2HqWtwvquTk+M4ZdwQThkbT9rYeEYM7nfcddXVN/BBXgkrtx3k9e0FHDhcRWSEcNr4oSyaPozzTkgmeWBMwGXXZRVy3T82MjVlIE9cM4e4EL9O07UsMZjjWvNxAd99YhNfOHkE9192ktfhtFl9g5Ke7eOZDXtZtb2AugZl9pghXJE2isUnDgv5AdpfWVUt96/YwRPvOVUs9116Ip+bkNBp2/NXWVPP5r2HyMgrYcPuUjbtLqW8ug6AlEExx84oThkXz6SkOGrqG3g7p4gV2w6y+uMCSitqiY6K4KxJiSyeNoz5U5MY3L9t1UOrthfw3Sc2MnPUYJZ9cw4DuuHFdOOwxGBa9NT7e7j1pY+YPmIQj39jTretPy4qr+aFTfn8a8NedvmO0jcqgnMnJ7FkZgrnTEkipk/oqprWZhVyywsfcfBIFd88fRw/OW+ypxeL6xuUHQePsOETJ1Fs+KSEwrJqwLlW0dCgHK2pJy46ivlTk1g0bRhnT07scCuj1z46wPef2sSccfE8dvUczy+Um46xxGA+Q1X53aqd/PGNHM6ZnMifvzKrR/z6U1U27TnEK1v28+rW/RSV1xAbHcWiacO4eGYKp08YSlRkx27ZKT1aw92vbueFD/eRmhTLLy87iZM7+P/XnUlVyS+tPFb1FCFw3rRhnDZ+KH2jQtO7/ksf7uOGZzdzxsQE/v71tJAmXtM1LDGYJmrrG7j5hY94bmM+V6SN4t4vTO/wwTKc1dU38O6uYpZv3s+KzIOUVdUxdEBfLjxpOBfPSGHW6CFEtLHp62sfHeC2l7dxqKKW/5o3ge+dO9HTC97h4NkNe/nZ81tZMDWJv351dsiSjukalhjMMUer6/juk5tYv9PH9QtS+dH8VNwbCnu0qtp61mX5eGXLflZ/XEB1XQMjBvfjohkpLJmZwpRhcQH3Q+GRKm57OZMVmQc5ccQg7r/0JE5I6bzeZrubf763m/95aRvnTx/Gn758co/8gdFTWWIwgHMD2zcf38DHB8r43y9M54pTRnsdkifKq+t4PfMgy7fsJz27iPoGJTUpliUzU7h4xghGD+2PqvLcxnzufnU7VXUN3LBgEt86c5wd+AJ45K1PuPvV7Vw8I4XfXTEzrG9ANJ+yxGDI9ZWz9NEPKC6v4a9fncU5UwL1it77FJdX89q2g7yyeT8f5JUAMGPUYPr3ieTdXcWcMnYI9116EhMSYz2ONLw9sC6X+1fs4LLZI/nlpSe1uYrOeKetiaH7X3k0AW3cXcq1yzYQIcK/rpvLjFGDvQ4pbAyNjeaquWO4au4Y9h2q5NUt+1m+ZT+ZvnLuvHgaV80dYwe5NvjuvAlU19Xz+9XZ9I2K4N5Lpoe8irLgSBURIiTE9u0V1Z/hwhJDD7Qy8yA/fPpDhg+KYdk35zBmaHh0dRGORgzux7fPnsC3z56AqtrBp51+ND+V6roGHliXS3RUBLd9/oSg92F2QRkrth1kReZBMvc73XTE9Ilg5JD+jBrSz3mO78eoIf2PDQ/q18feuxCyxNDD/PO93dz+8jZOGjmYR5amMTTWOkBrKzuwtJ+I8LNFk6mpa+CRtz6hb1QENy2e0q59qaps23eEFZkHWLHtILludyCzxwzh5vOnENMnkr0lFeSXVrK3tIKNu0s5UlXXZB2x0VGM/EzS6MeoeOfZ7thuH0sMPYSq8suVWTywLpcFU5P405dn2U1IpkuICLdeOJXqunr+9uYuYqIiuWHhpOMuU9+gbNpTyv99dJCVmQfZd6iSyAhh7vh4rj593HG76QA4XFlLfqmbLNykkV9awd6SCt7JLaKipr5J+RmjBnPxjBQuOmk4ScdZr3HYxeceoKaugZue38oLH+7jK6eO5q6Lp1lLGtPlGhqUm17YyrMZ+fx00WS+d07TfwOsrW/g3dxiVrhdexeVV9M3KoKzUhNYNG0YC6YmMyQEd+GrKqUVtW6iqCTXV85Kt1pKBOaOG8rFM1M4f/qwNncL0lNYq6Reoqyqlu8+sYm3coq48bxJfO+ciVYlYjxT36D85NnNvLR5P7deOJWvzR3D+p0+VmQeZPX2Ao5U1dG/byTnTEli8bRhnDMlqcv+yCinsJxXtuznlS372VV0lD6RwlmpiVw8M4UFU5N7RC8ArbHE0AsUHKni6sc2kF1Qxi++eCKXp41qfSFjOlldfQM/+tdm/vPRAfr1iaSytp5B/fqwYGoyi6cP48zUBE+701BVMvcfYbmbJA4criKmTwQLpiZz8YwUzp6c2GPvcLfE0MPlFJax9NENHKqo4a9fm83ZkxK9DsmYY2rrG7j71e3UNyiLpw9j7vih9AnD6s2GBiVjdynLt+zjtY8OUnK0hriYKBa7/WydNr7j/WyFI0sMPVhtfQOn3/cGCjx29SlMHzHI65CM6fZq3a7KX9lygJWZBymvriMhti8Xnjici2akdOq/6XUVu8GtB9u89xCFZdU88NVZlhSMCZE+kRHMm5zEvMlJ3Fs7nXVZhSzfsp9/bdjLsnd3EyEwOr4/ExJjmZgUy4Sk2GPDg/r1rOawlhi6ofSdPiIEPjexa/4kxpjeJqZPJIunD2fx9OGUVdWSnl3EjoNl5BaWk+srJz27iJr6T/+3OzEumomJsUxIGsDExFgmJsUxMSmW5IHR3bIxSNCJQUTigWeAsUAe8CVVLQ1Qbilwqzt6j6ouazZ/OTBeVacHG1NPtz67iJmjBve4XynGhKO4mD5ccOJwLjhx+LFp9Q3K3pIKcgrLyfGVk+s+v7x5P2V+N9/FRkcxIXEAE5JimTIsjstnjwpJk9zOFoozhpuANap6n4jc5I7/3L+AmzxuB9IABTaKyPLGBCIiXwTKQxBLj3e4opat+Yf4wbmpXodiTK8VGSGMTRjA2IQBLCD52HRVxVdWTY57ZtGYON7OKeKFTfv4y9pcrl+QytfmjgnLi/GNQpEYlgDz3OFlwDqaJQZgEbBKVUsARGQVsBh4WkRigR8D1wHPhiCeHu2d3CIaFM6aZNVIxoQbESFpYAxJA2M+U9W74+AR7n51O3e+sp0n39/DrRdOZd7k8OzxOBQpK1lVDwC4z4Fe6Qhgr994vjsN4G7gN0DF8TYiIteJSIaIZPh8vuCj7qbWZxcRFx3FjJHWW6ox3cmUYQN54ppT+fvX06irb+Dqxzbwjcc+IKcw/CpL2pQYRGS1iGwL8FjSxu0EuvqiIjITmKiqL7a2AlV9SFXTVDUtMbF3ttlXVdbv9HFaEP9hbIzxjoiw8IRkVt5wFrdcMJWMvFIW/349d76SyeGKWq/DO6ZNVUmquqCleSJSICLDVfWAiAwHCgMUy+fT6iaAkThVTqcBs0Ukz40lSUTWqeo8zGfkFVew71Al35k3wetQjDFBiI6K5FtnjecLs0bwm9d3suydPF78cB8/XjiJr8wZ7fkPv1BsfTmw1B1eCrwcoMxK4DwRGSIiQ4DzgJWq+oCqpqjqWOAMYKclhZalZztVaGel2vUFY3qChNhofvHFE3n1B2cyddhAbns5kwv+mH7su+6VUCSG+4CFIpINLHTHEZE0EXkYwL3ofDewwX3c1Xgh2rTd+p1FjI7vb3+8Y0wPc0LKQJ761qk8+LXZVNU2cNUjH3Dtsg3s8nlz/cG6xOgmausbmHnn61xy8gju/cKJXodjjOkk1XX1PPZ2Hn9+I4fqunqWnjaWH8xPDcl9S23tEsOuYHYTH+45xNGaes5M7Z0X3o3pLaKjIvnO2RN448az+eLJI3nk7U8459freOK93dQ3dM0PeUsM3UR6to/ICOG0CUO9DsUY0wWS4mK4/7KTeOX7ZzAxKZZbX9rGhX9M75LmrZYYugnrBsOY3mn6iEE8c91cHvjqLGL6RJI0sPP/x9060esGDlXUsDX/ED+ab91gGNMbiQjnnzicxdOHdUmnfHbG0A28k1uMKnZ9wZherqt6arXE0A2kZ/uIi4lixkj77wVjTOezxBDmnG4wivicdYNhjOkidqQJc58UHWXfoUqrRjLGdBlLDGEuPbsIgLMsMRhjuoglhjCXnu1jzND+jB7a3+tQjDG9hCWGMFZT18C7ucWcaZ3mGWO6kCWGMPbhnlLrBsMY0+UsMYSx9Owi6wbDGNPlLDGEsfRsHyePGszAGOsGwxjTdSwxhKnSozVs3XeYM+z6gjGmi1liCFPWDYYxxiuWGMKUdYNhjPGKJYYwpKqkZxdx+oQE6wbDGNPl7KgThnY1doMxya4vGGO6niWGMJS+0wdYNxjGGG9YYghD6dlFjB3an1Hx1g2GMabrBZUYRCReRFaJSLb7PKSFckvdMtkistRvel8ReUhEdorIDhG5NJh4eoKaugbe3VVsrZGMMZ4J9ozhJmCNqqYCa9zxJkQkHrgdOBWYA9zul0BuAQpVdRJwAvBmkPF0e5v2lFJRU2/9IxljPBNsYlgCLHOHlwGXBCizCFilqiWqWgqsAha7874J/AJAVRtUtSjIeLq99GyfdYNhjPFUsIkhWVW/2YQFAAASs0lEQVQPALjPSQHKjAD2+o3nAyNEZLA7freIbBKRf4tIcksbEpHrRCRDRDJ8Pl+QYYev9OwiTh41mDjrBsMY45FWE4OIrBaRbQEeS9q4jUD/Xq1AFDASeFtVZwHvAr9uaSWq+pCqpqlqWmJiz6x/Lz1aw0f7Dtv1BWOMp6JaK6CqC1qaJyIFIjJcVQ+IyHCgMECxfGCe3/hIYB1QDFQAL7rT/w1c07awe6a3c4ucbjDs/gVjjIeCrUpaDjS2MloKvBygzErgPBEZ4l50Pg9YqaoKvMKnSWM+sD3IeLq19J1FDIyJ4qQR1g2GMcY7wSaG+4CFIpINLHTHEZE0EXkYQFVLgLuBDe7jLncawM+BO0RkK3AV8JMg4+m2nG4wfJw+0brBMMZ4q9WqpONR1WKcX/rNp2cA1/qNPwo8GqDcbuCsYGLoKXJ9R9l/uIrvn2vXF4wx3rKfpmEiPdtpaWX3LxhjvGaJIUykZxcxLmGAdYNhjPGcJYYwUF1Xz7u5xXa2YIwJC5YYwsCm3YeorK3njImWGIwx3rPEEAasGwxjTDixxBAG0rOLmDXausEwxoQHSwweKzlaw7b91g2GMSZ8WGLw2Ns5bjcYduHZGBMmLDF4LD3b53SDMXJw64WNMaYLWGLwkNMNRhFnpCYQGRGoE1pjjOl6lhg8lOsr58DhKru+YIwJK5YYPLR+p/OHdXb/gjEmnFhi8FB6to/x1g2GMSbMWGLwSHVdPe/tKuEMa41kjAkzlhg8snF3KZW19XZ9wRgTdiwxeCQ9u4ioCGHu+HivQzHGmCYsMXgkPdvHrNFDrBsMY0zYscTggeLyajL3H7G7nY0xYckSgwfezi12usGYZNcXjDHhxxKDB9J3+hjUrw8njhjkdSjGGPMZlhi6WFlVLWt2FHLGROsGwxgTnoJODCISLyKrRCTbfR7SQrmlbplsEVnqN/3LIvKRiGwVkRUi0qMr3v+4JpvSihquO2u816EYY0xAoThjuAlYo6qpwBp3vAkRiQduB04F5gC3i8gQEYkC/gCco6onAVuB74cgprCUU1jGY2/n8aXZo5gxynpTNcaEp1AkhiXAMnd4GXBJgDKLgFWqWqKqpcAqYDEg7mOAiAgwENgfgpjCjqpy5yvb6dc3kp8unux1OMYY06JQJIZkVT0A4D4nBSgzAtjrN54PjFDVWuC7wEc4CeEE4JEQxBR2VmYWkJ5dxI8XTiIhNtrrcIwxpkVtSgwislpEtgV4LGnjdgJdZVUR6YOTGE4GUnCqkm5uIYbrRCRDRDJ8Pl8bNxseqmrruec/25mcHMdVc8d4HY4xxhxXVFsKqeqCluaJSIGIDFfVAyIyHCgMUCwfmOc3PhJYB8x015/rrutZAlyjcMs8BDwEkJaWpm2JO1w8+GYu+aWVPP2tuURFWkMwY0x4C8VRajnQ2MpoKfBygDIrgfPcC85DgPPcafuAE0Sk8U6vhcDHIYgpbOwtqeCBdblceNJwTpsw1OtwjDGmVW06Y2jFfcCzInINsAe4HEBE0oDvqOq1qloiIncDG9xl7lLVErfcncB6EakFdgNXhyCmsHHvfz4mQoRbLpjqdSjGGNMmQScGVS0G5geYngFc6zf+KPBogHIPAg8GG0c4Ss/2sSLzIDeeN4mUwf28DscYY9rEKrw7SU1dA3csz2TM0P5ce6bdzGaM6T4sMXSSZe/kkes7ym2fP4GYPpFeh2OMMW1miaETFB6p4g9rsjlnciLzpyZ7HY4xxrSLJYZOcN+KHdTUNXDbRdO8DsUYY9rNEkOIbdxdwgub9nHNmeMYlzDA63CMMabdLDGEUH2DcvvyTIYNjOH750z0OhxjjOkQSwwh9MyGvWzbd4SbL5jCgOhQ3CJijDFdzxJDiByqqOFXK3cwZ1w8F89I8TocY4zpMEsMIfKb13dyuLKWOy6ahtODuDHGdE+WGEJg+/4jPPn+br42dwwnpAz0OhxjjAmKJYYgqSp3LM9kcP++/HjhJK/DMcaYoFliCNLyLfv5IK+Eny6azOD+fb0OxxhjgmaJIQhHq+v439c+5sQRg/hS2iivwzHGmJCwNpVB+NMbORQcqeaBr80mMsIuOBtjegY7Y+igXF85j7y1i0tnjWTW6CFeh2OMMSFjiaEDVJW7XtlOdFQkPz9/stfhGGNMSFli6IDVHxfy5k4f1y9IJSkuxutwjDEmpCwxtFNVbT13v7qdiUmxLP3cWK/DMcaYkLOLz+30cPou9pRU8MQ1p9In0vKqMabnsSNbOzQ0KMve3c05kxM5IzXB63CMMaZTWGJoh+0HjuArq+bCk6yTPGNMz2WJoR3WZRUCcPakRI8jMcaYzhNUYhCReBFZJSLZ7nPABv0iskJEDonIq82mjxOR993lnxGRsO5TYm2Wj5NGDiIxLtrrUIwxptMEe8ZwE7BGVVOBNe54IL8Crgow/X7gd+7ypcA1QcbTaUqP1vDhnlLm2dmCMaaHCzYxLAGWucPLgEsCFVLVNUCZ/zRx/rTgXOC51pYPB+uzfTQozJuS5HUoxhjTqYJNDMmqegDAfW7PUXMocEhV69zxfGBES4VF5DoRyRCRDJ/P1+GAO2pdlo8h/fswY+TgLt+2McZ0pVbvYxCR1cCwALNuCXLbgXqd05YKq+pDwEMAaWlpLZbrDA0Nyps7fZw9KdE6yzPG9HitJgZVXdDSPBEpEJHhqnpARIYDhe3YdhEwWESi3LOGkcD+dizfZbbuO0zJ0RrOsWokY0wvEGxV0nJgqTu8FHi5rQuqqgJrgcs6snxXWrujEBE4M9UuPBtjer5gE8N9wEIRyQYWuuOISJqIPNxYSETSgX8D80UkX0QWubN+DvxYRHJwrjk8EmQ8nWJdViEzRw0mfkBYt6Y1xpiQCKqvJFUtBuYHmJ4BXOs3fmYLy+8C5gQTQ2crKq9m677D3LDA/s/ZGNM72J3PrVi/04cqnDPZri8YY3oHSwytWJvlIyE2mmkpA70OxRhjuoQlhuOoq29gvdtMNcKaqRpjeglLDMexee8hDlfWcs4Ua41kjOk9LDEcx7osH5ERwpkTLTEYY3oPSwzHsTarkNmjhzCofx+vQzHGmC5jiaEFBUeqyNx/hHlWjWSM6WUsMbTgzSyno755k6yZqjGmd7HE0IJ1OwtJHhjN1OFxXodijDFdyhJDALX1DaTvLOKcyUk4fxthjDG9hyWGADbuLqWsuo55drezMaYXssQQwNqsQqIihNMnDvU6FGOM6XKWGAJYt8PHKWPjiYuxZqrGmN7HEkMz+w9VklVQZnc7G2N6LUsMzaxzm6lab6rGmN7KEkMza7MKGTG4HxOTYr0OxRhjPGGJwU91XT1v5xQxb3KiNVM1xvRalhj8ZOSVUlFTb9VIxphezRKDn7U7CukbGcHnrJmqMaYXs8TgZ21WIaeOj6d/36D+CtsYY7o1SwyuPcUV5PqOWjWSMabXCyoxiEi8iKwSkWz3eUgL5VaIyCERebXZ9CdFJEtEtonIoyLi2R1l63YWAjBvst2/YIzp3YI9Y7gJWKOqqcAadzyQXwFXBZj+JDAFOBHoB1wbZDwdti7Lx5ih/RmXMMCrEIwxJiwEmxiWAMvc4WXAJYEKqeoaoCzA9NfUBXwAjAwyng6pqq3nnVzrTdUYYyD4xJCsqgcA3OcOVdC7VUhXASuOU+Y6EckQkQyfz9ehYFvy3q5iqmobrBrJGGOAVpvfiMhqYFiAWbeEMI6/AutVNb2lAqr6EPAQQFpamoZw26zL8hHTJ4K5462ZqjHGtJoYVHVBS/NEpEBEhqvqAREZDhS2NwARuR1IBL7d3mVDZV1WIaeNH0pMn0ivQjDGmLARbFXScmCpO7wUeLk9C4vItcAi4Muq2hBkLB3ySdFR8oorOGeKNVM1xhgIPjHcBywUkWxgoTuOiKSJyMONhUQkHfg3MF9E8kVkkTvrQSAZeFdENovIbUHG025rd7jNVCdZYjDGGGhDVdLxqGoxMD/A9Az8mp6q6pktLO/5LcZrswqZkDiA0UP7ex2KMcaEhV5953NFTR3v7yqxu52NMcZPr04M7+YWU1PfwDxLDMYYc0yvTgxrswrp3zeSU8YF7MnDGGN6pV6bGFSVtTt8nD4xgegoa6ZqjDGNem1iyCksZ9+hSru+YIwxzfTaxLAuy+lWw7rBMMaYpnptYlibVcjk5DhSBvfzOhRjjAkrvTIxlFXVsiGvhHlT7GzBGGOa65WJ4e2cYmrr1a4vGGNMAL0yMazLKiQuOorZY6yZqjHGNNfrEoOqsi7LxxmpCfSJ7HUv3xhjWtXrjow7DpZx8EiVVSMZY0wLel1iWJvl9KZ6tjVTNcaYgHpdYli3w8e0lIEkD4zxOhRjjAlLvSoxHK6sZeOeUqtGMsaY4+hVieGt7CLqG9TudjbGmOPoVYlhbVYhg/r1YeaowV6HYowxYatXJYbxiQP4yqmjibJmqsYY0yLP/1qzK/3XvIleh2CMMWHPfjobY4xpwhKDMcaYJoJKDCISLyKrRCTbfQ7Y+ZCIrBCRQyLyagvz/yQi5cHEYowxJjSCPWO4CVijqqnAGnc8kF8BVwWaISJpgDUTMsaYMBFsYlgCLHOHlwGXBCqkqmuAsubTRSQSJ2n8LMg4jDHGhEiwiSFZVQ8AuM/tvaX4+8DyxnUcj4hcJyIZIpLh8/k6EKoxxpi2aLW5qoisBoYFmHVLMBsWkRTgcmBeW8qr6kPAQwBpaWkazLaNMca0rNXEoKoLWponIgUiMlxVD4jIcKCwHds+GZgI5IgIQH8RyVFVu9nAGGM8FOwNbsuBpcB97vPLbV1QVf+D35mIiJS3NSls3LixSER2tzPWrpQAFHkdRBt1l1gtztDqLnFC94m1O8Q5pi2FRLXjtTIiMhR4FhgN7AEuV9USt6XRd1T1WrdcOjAFiAWKgWtUdWWzdZWramyHgwkjIpKhqmlex9EW3SVWizO0ukuc0H1i7S5xtkVQZwyqWgzMDzA9A7jWb/zMNqyrRyQFY4zp7uzOZ2OMMU1YYugcD3kdQDt0l1gtztDqLnFC94m1u8TZqqCuMRhjjOl57IzBGGNME5YYjDHGNGGJIUgiMkpE1orIxyKSKSI/cqffISL7RGSz+7ggDGLNE5GP3Hgy3Glt6iG3C2Oc7LfPNovIERG5Plz2p4g8KiKFIrLNb1rAfSiOP4pIjohsFZFZHsf5KxHZ4cbyoogMdqePFZFKv337oMdxtvhei8jN7v7MEpFFXRXncWJ9xi/OPBHZ7E73bJ+GhKraI4gHMByY5Q7HATuBE4A7gBu9jq9ZrHlAQrNpvwRucodvAu73Ok6/2CKBgzg35YTF/gTOAmYB21rbh8AFwP8BAswF3vc4zvOAKHf4fr84x/qXC4P9GfC9dr9XW4BoYByQC0R6GWuz+b8BbvN6n4biYWcMQVLVA6q6yR0uAz4GRngbVbu0qYdcj8wHclU1bO5yV9X1QEmzyS3twyXAP9TxHjDY7TrGkzhV9XVVrXNH3wNGdkUsx9PC/mzJEuBfqlqtqp8AOcCcTguumePFKk6/Pl8Cnu6qeDqTJYYQEpGxOH1Ave9O+r572v6o11U0LgVeF5GNInKdOy3YHnI705U0/aKF2/5s1NI+HAHs9SuXT/j8aPgmztlMo3Ei8qGIvCkird6Q2gUCvdfhvD/PBApUNdtvWrjt0zazxBAiIhILPA9cr6pHgAeACcBM4ADOaabXTlfVWcD5wPdE5CyvA2qJiPQFLgb+7U4Kx/3ZGgkwzfP24SJyC1AHPOlOOgCMVtWTgR8DT4nIQK/io+X3Oiz3p+vLNP0RE277tF0sMYSAiPTBSQpPquoLAKpaoKr1qtoA/J0uPOVtiarud58LgRdxYiporN6Q9veQ25nOBzapagGE5/7009I+zAdG+ZUbCezv4tiaEJGlwOeBr6pbGe5WzRS7wxtx6u4neRXjcd7rsNufACISBXwReKZxWrjt0/ayxBAkt27xEeBjVf2t33T/uuQvANuaL9uVRGSAiMQ1DuNciNzGpz3kQjt7yO1kTX6Bhdv+bKalfbgc+LrbOmkucFjb8KdUnUVEFgM/By5W1Qq/6Yni/JsiIjIeSAV2eRPlcd/r5cCVIhItIuNw4vygq+MLYAGwQ1XzGyeE2z5tN6+vfnf3B3AGzunsVmCz+7gA+CfwkTt9OTDc4zjH47To2AJkAre404fi/F93tvscHwb7tD9OL7yD/KaFxf7ESVYHgFqcX7DXtLQPcao+/oLza/EjIM3jOHNw6ugbP6cPumUvdT8TW4BNwEUex9nie43zB2G5QBZwvtfvvTv9cZzepP3LerZPQ/GwLjGMMcY0YVVJxhhjmrDEYIwxpglLDMYYY5qwxGCMMaYJSwzGGGOasMRgjDGmCUsMxhhjmvh/sAjT0xqm4bUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nb_estimators, r2)\n",
    "plt.title('R² score over the number of estimators')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 645,
   "metadata": {},
   "outputs": [],
   "source": [
    "best_n = nb_estimators[np.argmax(r2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 646,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best number of estimator is: 60\n"
     ]
    }
   ],
   "source": [
    "print('The best number of estimator is:', best_n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I now train the best model on the whole training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 684,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train, X_train, Y_test, X_test = train_val_test_split(X,Y,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 685,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BaggingRegressor(base_estimator=None, bootstrap=True,\n",
       "         bootstrap_features=False, max_features=1.0, max_samples=1.0,\n",
       "         n_estimators=10, n_jobs=1, oob_score=False, random_state=12,\n",
       "         verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 685,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = BaggingRegressor(n_estimators = best_n, random_state = 12)\n",
    "model.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 686,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 689,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R² score for this model is: 0.08374729222238819\n"
     ]
    }
   ],
   "source": [
    "r2_bag = r2_score(Y_test,Y_pred)\n",
    "print('The R² score for this model is:',r2_bag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 690,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The money made with this model is: 2.4648655048763275\n"
     ]
    }
   ],
   "source": [
    "money_bag = money_made(Y_pred,Y_test)\n",
    "print('The money made with this model is:',money_bag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient Boosting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will perform a grid search with Gradient Boosting to find the best trade off between the learning rate and the number of estimators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 653,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train, X_train, Y_val, X_val, Y_test, X_test = train_val_test_split(X,Y,test_size = 0.2,val = True, val_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 654,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_estimators = np.arange(10,110,10)\n",
    "learning_rates = np.array([0.001,0.01,0.1,1,10,100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 662,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\sklearn\\ensemble\\gradient_boosting.py:282: RuntimeWarning: overflow encountered in square\n",
      "  np.sum(sample_weight * ((y - pred.ravel()) ** 2.0)))\n",
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\numpy\\core\\_methods.py:32: RuntimeWarning: overflow encountered in reduce\n",
      "  return umr_sum(a, axis, dtype, out, keepdims)\n",
      "C:\\Users\\antoi\\Anaconda3\\lib\\site-packages\\sklearn\\metrics\\regression.py:538: RuntimeWarning: overflow encountered in square\n",
      "  numerator = (weight * (y_true - y_pred) ** 2).sum(axis=0,\n"
     ]
    }
   ],
   "source": [
    "r2 = np.zeros((len(nb_estimators),len(learning_rates)))\n",
    "for i in range(len(nb_estimators)):\n",
    "    for j in range(len(learning_rates)):\n",
    "        model = GradientBoostingRegressor(n_estimators = nb_estimators[i],learning_rate = learning_rates[j],random_state = 630)\n",
    "        model.fit(X_train,Y_train)\n",
    "        Y_pred = model.predict(X_val)\n",
    "        r2[i,j] = r2_score(Y_val,Y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 663,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best number of estimators is: 10\n"
     ]
    }
   ],
   "source": [
    "best_n = nb_estimators[np.unravel_index(np.argmax(r2, axis=None), r2.shape)[0]]\n",
    "print('The best number of estimators is:',best_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 664,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best learning rate is: 0.1\n"
     ]
    }
   ],
   "source": [
    "best_rate = learning_rates[np.unravel_index(np.argmax(r2, axis=None), r2.shape)[1]]\n",
    "print('The best learning rate is:',best_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We now train the best model on the whole training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 691,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train, X_train, Y_test, X_test = train_val_test_split(X,Y,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 692,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,\n",
       "             learning_rate=0.1, loss='ls', max_depth=3, max_features=None,\n",
       "             max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
       "             min_impurity_split=None, min_samples_leaf=1,\n",
       "             min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "             n_estimators=10, presort='auto', random_state=630,\n",
       "             subsample=1.0, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 692,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = GradientBoostingRegressor(n_estimators = best_n, learning_rate = best_rate,random_state = 630)\n",
    "model.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 693,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 696,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R² score for this model is: 0.10423488009750992\n"
     ]
    }
   ],
   "source": [
    "r2_grad = r2_score(Y_test,Y_pred)\n",
    "print('The R² score for this model is:',r2_grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 697,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The money made with this model is: 2.530627762427387\n"
     ]
    }
   ],
   "source": [
    "money_grad = money_made(Y_pred,Y_test)\n",
    "print('The money made with this model is:',money_grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Models Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 706,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2_scores = [r2_lin, r2_las, r2_bag, r2_grad]\n",
    "moneys = [money_lin, money_las, money_bag, money_grad]\n",
    "models = ['Linear', 'Lasso', 'Bagging', 'Gradient Boosting']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 709,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(4)\n",
    "plt.subplot(211)\n",
    "plt.bar(x, height= r2_scores) \n",
    "plt.xticks(x, models)\n",
    "plt.subplot(212)\n",
    "plt.bar(x, height = moneys)\n",
    "plt.xticks(x, models)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model that has the best R² score is the lasso regression which mean that it explains the the variance the best. And the model with which we make the more money is the gradient boosting."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}